The randomness of it can be beneficial, interesting, listening to highly contrasting Psalms, one after another can be jarring, in a good way.
Someone in response to one of the videos I posted of Walter Brueggemann talking about Psalm 73 came up with one of the stupider lines from Brit TV comedy about how tiresome the Psalms are, I don't know how anyone who really paid attention to them could think they were tiresome. Going through them can be like a exercise in emotional and intellectual stretching, as Brueggemann suggested in one lecture or interview, trying to imagine what would bring someone to say what is said in them, it can be an exercise in both empathic imagination and self-reflection. I suspect doing that would be both a lot more useful and a lot cheaper than going to see a shrink, though, since they don't charge you three figures an hour to convince you that someone else is the reason you're unhappy, it wouldn't be as superficially gratifying. I can imagine many of the texts of the Bible and other scriptures could do the same. I can well imagine going through Suras of the Koran or scriptures from another religion in a similar way, given similar depth and contrast.
This short excerpt in which Brueggemann talks about the Psalms of Vengeance and how they could be used is a good way to deal with some of the most troubling of the texts.
One of my posts last week contained an excerpt that discussed the genocidal General Trotha accusing the Christian missionaries of whipping up the Herero people he was murdering with bloodthirsty passages from the Jewish scriptures, which is a pretty telling thing for a man responsible for scores of thousands of murders to accuse someone else of, as if people under an oppressive colonial regime which is enslaving and killing them couldn't get those ideas all on their own. It certainly isn't how most people, even oppressed people have reacted to those texts. They have a far deeper, far more serious use than the anti-religious bigots, either murderous colonial generals from the 19th century or tedious Brit-atheist comedians of the 1970s would like them to have. I'm finding that they are a far deeper mental workout than the alternatives. They're certainly a far deeper spiritual tool than a very partial, very superficial reading of them could find.